Question

You are 10 m away from a sound source of
intensity comparable to the background
noise in a very quiet room (20 dB). If you
want the intensity in dB to double, you must
move to a distance ...
A) 100 m
B) 20 m
C) 7 m
D) 5 m
E) 1 m

the answer is 1 m, but I'm not sure how to approach this question. I've tried using these 2 formulas, but I'm not really getting anywhere:
--> I α 1/r^2
--> I(dB) = 10log(I/Io)

Please help!

Answer 1

20 db = 10 log (I/Io)
so
log (I/Io) = 2
so
I/Io = 10^2
now do 40 db
40 db = 10 log (I/Io)
log I/Io = 4
I/Io = 10^4
the ratio of intensities = 10^4/10^2 =100
so
r^2/(10^2) = 1/100
r^2 = 1
r = 1

Answer 2

If you had said "Physics" instead if "please help" I would have seen this earlier.